Week of Events
Applied Math Talk: Nonlocal problems for linear evolution equations (Prof. Smith David Andrew, Yale-NUS College, Singapore)
Applied Math Talk: Nonlocal problems for linear evolution equations (Prof. Smith David Andrew, Yale-NUS College, Singapore)
Linear evolution equations, such as the heat equation, are commonly studied on finite spatial domains via initial-boundary value problems. In place of the boundary conditions, we consider “multipoint conditions”, where one specifies some linear combination of the solution and its derivative evaluated at internal points of the spatial domain, and “nonlocal” specification of the integral […]
Theory of vertex Ho-Lee-Schur graphs (Sin-Min Lee, SJSU)
Theory of vertex Ho-Lee-Schur graphs (Sin-Min Lee, SJSU)
A triple of natural numbers (a,b,c) is an S-set if a+b=c. I. Schur used the S-sets to show that for n >3, there exists s(n) such that for prime p > s(n), x^p + y^p = z^p (mod p) has a nontrivial solution. A (p,q)-graph G is said to be vertex Ho-Lee-Schur graph if there exists a bijection […]
A Conformal Mapping Approach to Shape Optimization Problems. (Kao, CMC)
A Conformal Mapping Approach to Shape Optimization Problems. (Kao, CMC)
Abstract: In this talk, a conformal mapping approach to shape optimization problems on planar domains will be discussed. In particular, spectral methods based on conformal mappings are proposed to solve Steklov eigenvalues and their related shape optimization problems in two dimensions. To apply spectral methods, we first reformulate the Steklov eigenvalue problem in the complex domain […]
A (Z⊕Z)-family of knot quandles (Jim Hoste, Pitzer College)
A (Z⊕Z)-family of knot quandles (Jim Hoste, Pitzer College)
Suppose K is an oriented knot in a 3-manifold M with regular neighborhood N (K). For each element γ ∈ π 1 (∂N (K)) we define a quandle Q γ (K; M) which generalizes the concept of the fundamental quandle of a knot. In particular, when γ is the meridian of K, we obtain the […]